VSE Audio and Video Sync is off by 2 Frames Every Time
First off many others have had this problem.

Now you actually can set the Framerate Base with precision out to 6 places. (Go ahead and right now enter 1.00125 as the framerate base.)
Notice in this screen shot that blender knows that my custom frame rate is 23.97; yet it is still displaying that the framerate base is just 1.001.


Copy the line below into the Python Console then press Enter you will see what the value really is.
D.scenes['Scene'].render.fps_base